Rangers trail the Dons by nine points in the race to finish as Ladbrokes Premiership runners-up behind runaway leaders Celtic.
But as Pedro Caixinha’s men must play Aberdeen twice before the end of the campaign, there remains plenty of time for Rangers to claw their way back into contention.
The first of those meetings takes place in Aberdeen a week on Sunday, but beforehand Hodson and his colleagues must see off Motherwell and Kilmarnock.
And the Northern Irishman admits Rangers’ strength of conviction needs to stand up to the test.
Speaking ahead of Saturday’s visit of Well to Ibrox, Hodson said: “We’ve got to believe we can catch Aberdeen.
“In the last three games we’ve shown some real positive signs that we can push forward to where we want to be.
“If you go into games thinking you’re not going to win, that’s not right. You need to have that winning mentality.
“This week is massive. The first game is against Motherwell, then we’ve got Wednesday’s game down at Kilmarnock.
“If we can get six points there, going into the game with Aberdeen on Sunday, it’d put them under a lot of pressure.
“But we have to take it game by game. That’s all we can do at the moment and see where it takes us at the end of the season.”
A dark cloud may have hung over Rangers for much of their miserable campaign, but Hodson says the arrival of new boss Caixinha has lifted spirits.
“It’s always a happy place to come and work,” he insisted. “Who wouldn’t be happy coming to play for Rangers?
“It’s such a big club and obviously there have been hard times but as players you don’t want to lose games. It hurts when you do.
“But when times were hard we got together as a team and knuckled down in training and looked forward to the next game so we could put it right.
“There’s a new manager in now and that’s given the players a lift. That showed against Hamilton in his first game in charge. We put in a real strong performance.”
Caixinha has been quick to stamp his authority on his new squad, with the Portuguese implementing a six-day working week.
There has been no dissent from his new troops, though, and the likes of Hodson are looking at the change in management as an opportunity to impress.
Under former boss Mark Warburton, the former MK Dons defender had to endure a bit-part role but Hodson will get the chance to show the new man in charge what he can do against the Steelmen, as his right-back rival James Tavernier is suspended.
“When a new manager comes in, every player is being looked at.,” said the 25-year-old.
“It’s up to you as a player to try and catch the manager’s eye and impress him so you are the one who plays come Saturday.
“We’re still only three weeks in and everyone is playing for their places. Hopefully if I carry on training well I’ll get more game time.
“That’s down to the manager, though, and we’ll have to see how things go in the next couple of weeks.”